Added fast-exponentiation algorithm

README.md

@@ -60,7 +60,9 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Factorial](src/algorithms/math/factorial) 
   * `B` [Fibonacci Number](src/algorithms/math/fibonacci)
   * `B` [Primality Test](src/algorithms/math/primality-test) (trial division method)
-  * `B` [Euclidean Algorithm](src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
+  * `B` [Euclidean Algorithm](src/algorithms/math/euclidean-algorithm) - calculate the Greatest 
+  Common Divisor (GCD)
+  * `B` [Fast Exponentiation](src/algorithms/math/fast-exponentiation)
   * `B` [Least Common Multiple](src/algorithms/math/least-common-multiple) (LCM)
   * `B` [Sieve of Eratosthenes](src/algorithms/math/sieve-of-eratosthenes) - finding all prime numbers up to any given limit
   * `B` [Is Power of Two](src/algorithms/math/is-power-of-two) - check if the number is power of two (naive and bitwise algorithms)

src/algorithms/math/fast-exponentiation/README.md

@@ -0,0 +1,10 @@
+# Fast Exponentiation Algorithm
+The operation of modular exponentiation calculates the remainder when an integer `b` (the base) raised to the eth power (the exponent), be, is divided by a positive integer m (the modulus). In symbols, given base `b`, exponent e, and modulus m, the modular exponentiation `c` is: `c ≡ b^e (mod m)`. 
+
+# Modular Arithmetic
+- `(a + b) % m` = `( a%m + b%m ) % m`
+- `(a * b) % m` = `( a%m * b%m ) % m`
+
+
+## References
+- [Wikipedia](https://en.wikipedia.org/wiki/Modular_exponentiation)

src/algorithms/math/fast-exponentiation/__test__/fastExponent.test.js

@@ -0,0 +1,16 @@
+import fastExponent from '../fastExponent';
+
+describe('fastExponent', () => {
+  it('should calculate power using fast exponentiation algorithm', () => {
+    expect(fastExponent(5, 5)).toBe(3125);
+  });
+  it('should calculate power using fast exponentiation algorithm', () => {
+    expect(fastExponent(123, 4)).toBe(228886641);
+  });
+  it('should calculate power using fast exponentiation algorithm', () => {
+    expect(fastExponent(2, 15)).toBe(32768);
+  });
+  it('should calculate power using fast exponentiation algorithm', () => {
+    expect(fastExponent(43, 3)).toBe(79507);
+  });
+});

src/algorithms/math/fast-exponentiation/__test__/modularExponent.test.js

@@ -0,0 +1,16 @@
+import modularExponent from '../modularExponent';
+
+describe('modularExponent', () => {
+  it('should calculate power using fast exponentiation algorithm', () => {
+    expect(modularExponent(5, 5, 23)).toBe(20);
+  });
+  it('should calculate power using fast exponentiation algorithm', () => {
+    expect(modularExponent(123, 4, 10001)).toBe(3755);
+  });
+  it('should calculate power using fast exponentiation algorithm', () => {
+    expect(modularExponent(2, 15, 13)).toBe(8);
+  });
+  it('should calculate power using fast exponentiation algorithm', () => {
+    expect(modularExponent(43, 3, 1000000007)).toBe(79507);
+  });
+});

src/algorithms/math/fast-exponentiation/fastExponent.js

@@ -0,0 +1,20 @@
+/**
+ * @param {number} base
+ * @param {number} exponent
+ * @return {number}
+ */
+
+export default function fastExponent(base, exponent) {
+  let x = base;
+  let y = exponent;
+  let res = 1;
+
+
+  while (y > 0) {
+    if (y & 1) res *= x;
+    y >>= 1;
+    x *= x;
+  }
+
+  return res;
+}

src/algorithms/math/fast-exponentiation/modularExponent.js

@@ -0,0 +1,23 @@
+/**
+ * @param {number} base
+ * @param {number} exponent
+ * @param {number} m
+ * @return {number}
+ */
+
+export default function modularExponent(base, exponent, m) {
+  let x = base;
+  let y = exponent;
+  let res = 1;
+  const p = m;
+
+  x %= p;
+
+  while (y > 0) {
+    if (y & 1) res = (res * x) % p;
+    y >>= 1;
+    x = (x * x) % p;
+  }
+
+  return res;
+}